Reconstruction of Probability Phylogenetic Trees with Substitution Models

By the evolutionary theory all existing/extinct organisms are descended from a common ancestor. Hence, given a set of organisms, a phylogenetic tree (phylogeny) can be reconstructed showing the evolutionary relationships among a set of biological organisms. The commonly used methods for reconstruction do not make full use of the input information and uncertainty exists in the reconstructed trees. Recently the authors proposed a new probability representation model of phylogenetic trees, which is a natural and logical solution that overcomes the drawbacks in the currently used phylogeny reconstruction techniques. In this representation model the ancestor of any subset of given sequences is a matrix whose columns are probability distributions of nucleotides, and the Hamming distance between sequences becomes the statistical distance between these probability vectors. However, the Hamming distance often underestimates the number of substitutions really occurring in the evolutionary process. To solve this underestimation problem many substitution models have been established based on a Markov process. In this paper a systematic procedure for reconstruction of probability phylogenetic trees is developed in which a substitution model is used for deriving a modified statistical distance.